Samples where proceed or its synonyms are used according to this definition

We proceeded towards Washington

She continued in the direction of the hills

We are moving ahead in time now

Synonyms for proceed in the sense of this definition

(proceed is a kind of ...) change location; move, travel, or proceed, also metaphorically

"How fast does your new car go?""We travelled from Rome to Naples by bus""The policemen went from door to door looking for the suspect""The soldiers moved towards the city in an attempt to take it before night fell""news travelled fast"